This course is designed to provide students systematic understanding on quantum states of atoms and molecules and their interaction with optical fields, by extending the study on the microscopic fundamental laws, introduced in the preceding course: CHM.C201, “Introductory quantum chemistry.” The course is organized to develop students' abilities in the following four subjects:
1) Understanding fundamentals of angular momentum in quantum mechanics and applying them to solve basic problems relating various angular momenta appearing in atoms and molecules,
2) Utilizing the time-dependent perturbation theory and applying it to derive fundamental rules for optical transitions in atoms and molecules,
3) Understanding the quantum-mechanical description of magnetic interaction and understanding microscopic behavior of atoms and molecules under magnetic field,
4) Utilizing the aforementioned fundamental knowledge on quantum chemistry to establish detailed description of quantum states and optical transitions among them in atoms and molecules.
By the end of this course, students will be able to:
1) Understand how to utilize the basic principles of quantum chemistry, such as angular-momentum and perturbation theories, and apply them appropriately to various problems relating microscopic behavior of atoms and molecules,
2) Find out by themselves the way to explore microscopic properties of atoms and molecules and their reactivity, on the basis of clear understanding on atomic and molecular quantum states and their response to external stimulation such as optical and magnetic fields.
Physical chemistry, Quantum mechanics, Anugular momentum, Optical transitions, Atomic and molecular spectra
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
(1) At the biginning of each class, subjects of the previous class are reviewed briefly.
(2) Towards the end of class, students are given excercise problems related to what is taught on that day to solve.
(3) Students must familiarize themselves with topics described in the required learning section before comming to class.
|Course schedule||Required learning|
|Class 1||General theory on angular momentum (1) Angular momentum and its shift operators||Describe the commutation relation of angular momentum. Derivate matrix elements for the shift operators.|
|Class 2||General theory on angular momentum (2): Coupling of two angular momenta||Derive the values of total angular momentum composed with two angular momenta. Explain what the vector model for angular momentum is.|
|Class 3||General theory on angular momentum (3) Spin multiplicity and orbital and spin angular momenta||Describe the singlet and triplet spin functions. Explain the way for coupling of orbital and spin angular momenta.|
|Class 4||Absorption and emmision of light (1) Time-dependent perturbation theory||Describe the first-order correction for wave function by the perturbation theory. Calculate the change of eigen energy and wave function by the constant perturbation.|
|Class 5||Absorption and emmision of light (2) Derivation of optical transition rates||Describe the interaction term for optical transition. Explain what the Fermi’s golden rule is.|
|Class 6||Absorption and emmision of light (3) Stimulated absorption/emmision and spontaneous emission||Explain what the Einstein’s A and B constants are. Explain the wave-length dependence for spontaneous-emission probability.|
|Class 7||Magnetic property of atoms and molecules (1) Zeeman effects and magnetic resonance||Describe the Zeeman effect of atomic hydrogen. Explain the operation principle of electron spin resonance (ESR).|
|Class 8||Magnetic property of atoms and molecules (2) Spin-orbit interaction and LS coupling in atoms||Describe the operator for the spin-orbit interaction. Describe the LS coupling in atomic hydrogen.|
|Class 9||Atomic energy levels and spectra (1) Term symbols of atomic electronic states||Derive the term symbols for atoms in the first and the second lows.|
|Class 10||Atomic energy levels and spectra (2) Slater determinants and Hund's rule||Derive the Slater determinants of the excited states of He. Explain what the Hund’s rule is.|
|Class 11||Atomic energy levels and spectra (3) Selection rules for atomic absorption/emmision molecules||Describe the optical selection rules for atomic hydrogen. Explain what Rydberg states are.|
|Class 12||Molecular energy levels and spectra (1) Born-Oppenheimer approximation and hierarchy of energy levels||Describe the condition for satisfying the Born-Oppenheimer approximation. Explain the energy ordering for electronic, vibrational, and rotational motion.|
|Class 13||Molecular energy levels and spectra (2) Electronic states of diatomic molecules and Franck-Condon principle||Describe the electronic states of nitrogen molecule. Explain what the Franck-Condon principle is.|
|Class 14||Molecular energy levels and spectra (3) Molecular spectra for vibration and rotation||Describe the selection rules for vibrational transitions. Explain the relation between rotational spectra and molecular structure.|
|Class 15||Molecular energy levels and spectra (4) Relaxation processes in electronic excited states||Explain the relation between fluorescence life times and non-radiative transitions. Explain what internal conversion (IC) and intersystem crossing (ISC) are.|
Physical chemistry: A molecular approach, by D. A. McQuarrie and J. D. Simon, The University Science Books.
Physical chemistry, by P. W. Atkins, Oxford University Press.
Molecular Quantum Mechanics, by P. W. Atkins, Oxford University Press.
Students will be assessed on their understanding of fundamentals of quantum mechanics and their application to atomic/molecular systems.
Students' course scores are based on the final exam (60%) and exercise problems (40%).
No prerequisites are necessary, but enrollment in the related courses is desirable.
Contact by email in advance to schedule an appointment.
Yasuhiro Ohshima (West Building 4, Room 105B)